Topic 1: Be able to combine functions and determine the resulting function. Topic 2: Be able to find the product of functions and determine the resulting.

Topic 1: Be able to combine functions and determine the resulting function.

Topic 2: Be able to find the product of functions and determine the resulting function.Topic 3: Be able to perform multiple operations on functions.

Topic 4: Determine if two given functions represent equivalent forms of the same function..

I. Multiplying Polynomial Functions

Example 1: 3(2x + 6)

(3)(2x) + (3)(6)

6x + 18

Example 2: -5(3x2 – 6x + 4)

(-5)(3x2) + (-5)(– 6x) + (-5)(4)

-15x2 + 30x - 20

Concept: Constant x Linear = Linear

Concept: Constant x Quadratic = Quadratic

Example 3: 3(-4x3 - 7x2 + x + 2)

(3)(-4x3) + (3)(– 7x2) + (3)(x) + (3)(2)

-12x3 - 21x2 + 3x + 6

Concept: Constant x Cubic = Cubic

I. Multiplying Polynomial Functions

Example 4: (3x + 4)(2x - 1)

(3x)(2x - 1) + (4)(2x - 1)

(3x)(2x ) + (3x)(-1) (4)(2x ) + (4)(-1)+

6x2 - 3x + 8x - 4

6x2 + 5x - 4

3x 4

2x

-1

6x2 8x

-3x -4

6x2 + 5x - 4

Concept: Linear x Linear= Quadratic

Example 5: (-2x - 3)(6x + 7)

(-2x)(6x + 7) + (-3)(6x + 7)

(-2x)(6x ) + (-2x)(7) (-3)(6x ) + (-3)(7)+

-12x2 - 14x - 18x - 21

-12x2 - 32x - 21

-2x -3

6x

7

-12x2 -18x

-14x -21

-12x2 -32x - 21

Concept: Linear x Linear= Quadratic

I. Multiplying Polynomial Functions

Example 6: (x - 3)(2x2 – 7x + 5)

(x)(2x2 – 7x + 5) + (-3)(2x2 - 7x + 5)

(x)(2x2 )+ (x)(– 7x) + (x)( 5) (-3)(2x2 )+ (-3)(– 7x) + (-3)( 5) +

2x3 – 7x2 + 5x -6x2 + 21x - 15

2x3 – 13x2 + 26x - 15

2x2 -7x 5

x

-3

2x3 -7x2 5x

-6x2 21x -15

2x3 – 13x2 + 26x - 15

Concept: Linear x Quadratic = Cubic

I. Multiplying Polynomial Functions

Example 7: (5x2 - 3)(3x2 – 4x + 2)

5x2 0x -3

3x2

-4x

2

15x4 0x3 -9x2

-20x3 0x2 12x

10x2 0x -6

15x4 - 20x3 + x2 + 12x - 6

Concept: Quadratic x Quadratic = Quartic

Special Note: When setting up your table, be sure that you account for all terms of the polynomial.

I. Multiplying Polynomial Functions

Example 8: (4x2 – 3x + 2)(3x2 + 6x - 5)

4x2 -3x 2

3x2

6x

-5

12x4 -9x3 6x2

24x3 -18x2 12x

-20x2 15x -10

12x4 + 15x3 - 32x2 + 27x - 10

Concept: Quadratic x Quadratic = Quartic